Question: Evaluate limx->0 [(1/3+x)-(1/3) / (x)] Possible answers: a) -1/9 b) 0 c) 1/9 d) does not exist I believe the answer is a. Is this right? Any help is appreciated.
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That's correct.
Assuming that you mean lim(x->0) (1/(3+x))-(1/3))/x (notice the additional parentheses), then, yes, 1/9 is correct. But I first interpreted his as lim(x->0) ((1/3)+ x)- (1/3))/x and that has a limit of 1. Which did you mean?
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